Question

Following are the published weights (in pounds) of all of the team members of Football Team A from a previous year.

178; 203; 212; 212; 232; 205; 185; 185; 178; 210; 206; 212; 184; 174;
185; 242; 188; 212; 215; 247; 241; 223; 220; 260; 245; 259; 278; 270;
280; 295; 275; 285; 290; 272; 273; 280; 285; 286; 200; 215; 185; 230;
250; 241; 190; 260; 250; 302; 265; 290; 276; 228; 265

Organize the data from smallest to largest value.

• Part (a)

  Find the median.
  

• Part (b)

  Find the first quartile. (Round your answer to one decimal place.)
  

• Part (c)

  Find the third quartile. (Round your answer to one decimal place.)
  

• Part (d)

  Construct a box plot of the data.

• Part (e)

  The middle 50% of the weights are from   to   .

• Part (f)

  If our population were all professional football players, would the above data be a sample of weights or the population of weights? Why?

  The above data would be a sample of weights because they represent a subset of the population of all football players.The above data would be a population of weights because they represent all of the players on a team.     The above data would be a population of weights because they represent all of the football players.The above data would be a sample of weights because they represent all of the players from one year.

• Part (g)

  If our population were Football Team A, would the above data be a sample of weights or the population of weights? Why?

  The data would be a population of weights because they represent all of the professional football players.The data would be a sample of weights because they represent all of the professional football players.     The data would be a sample of weights because they represent all of the players on Football Team A.The data would be a population of weights because they represent all of the players on Football Team A.

• Part (h)

  Assume the population was Football Team A. Find the following. (Round your answers to two decimal places.)(i) the population mean, μ
    
  
  (ii) the population standard deviation, σ
    
  
  (iii) the weight that is 3 standard deviations below the mean
  
  
  (iv) When Player A played football, he weighed 200 pounds. How many standard deviations above or below the mean was he?

  standard deviations below  the mean

• Part (i)

  That same year, the average weight for Football Team B was 240.08 pounds with a standard deviation of 44.38 pounds. Player B weighed in at 209 pounds. Suppose Player A from Football Team A weighed 200 pounds. With respect to his team, who was lighter, Player B or Player A? How did you determine your answer?

  Player A, because he is more standard deviations away from his team's mean weight.Player B, because he is more standard deviations away from his team's mean weight.     Player A, because Football Team A has a higher mean weight.Player B, because Football Team B has a higher mean weight.

Answer 1

(a)

The median is the middle number in a sorted list of numbers.

Ordering the data from least to greatest,

174   178   178   184   185   185   185   185   188   190   200   203   205   206   210   212   212   212   212   215   215   220   223   228   230   232   241   241   242   245   247   250   250   259   260   260   265   265   270   272   273   275   276   278   280   280   285   285   286   290   290   295   302   

So median is 241

(b)

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers.

174   178   178   184   185   185   185   185   188   190   200   203   205   206   210   212   212   212   212   215   215   220   223   228   230   232   241   241   242   245   247   250   250   259   260   260   265   265   270   272   273   275   276   278   280   280   285   285   286   290   290   295   302   

So, the bottom half is

174   178   178   184   185   185   185   185   188   190   200   203   205   206   210   212   212   212   212   215   215   220   223   228   230   232   

The median of these numbers is 205.5.

(c)

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers.

174   178   178   184   185   185   185   185   188   190   200   203   205   206   210   212   212   212   212   215   215   220   223   228   230   232   241   241   242   245   247   250   250   259   260   260   265   265   270   272   273   275   276   278   280   280   285   285   286   290   290   295   302   

So, the upper half is

241   242   245   247   250   250   259   260   260   265   265   270   272   273   275   276   278   280   280   285   285   286   290   290   295   302   

The median of these numbers is 272.5.

(d)